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Math Help - Basic Properties of Number (Proof)

  1. #1
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    Exclamation Basic Properties of Number (Proof)

    I am not sure where to post this question, but it seems to require only algebra.

    The maximum of two numbers x and y is denoted by max(x,y). Thus max(-1,3) = max(3,3) = 3 and max (-1, -4) = max(-4, -1) = -1. The minimum of x and y is denoted by min(x,y). Prove that:

    max(x,y) = (x+y+abs(y-x))/2

    I was able to prove it if x = y but after that I don't know how to prove it.

    Thanks.
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  2. #2
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    Break it down into two cases,

    what happens when x \ge y?
    what happens when  x < y ?
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  3. #3
    Member Mollier's Avatar
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    What about saying that \frac{x+y+abs(y-x))}{2}=x.

    After some algebra you get that abs(y-x)=x-y \Rightarrow x\geq y.
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  4. #4
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    Thank you. I will give it another try.
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